Evaluate the following integral.

${\displaystyle \underset{-}{\overset{5}{}}}co{s}^{2}xdx$

$u=2x$

Find $du.$

$du=(2)dx$

Rewrite the second $of$ the two integrals found above using this change $of$ variables.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(\frac{1}{4}cosu)du$

$(Type$ exact answers.$)$

Evaluate the given definite integral.

${\displaystyle \underset{-}{\overset{5}{}}}co{s}^{2}xdx=$

$(Typean$ exact answer.$)$